A supplement to the Iomdin-Lê theorem for singularities with one-dimensional singular locus

To a germ $f: (ℂ^n,0) → (ℂ,0)$ with one-dimensional singular locus one associates series of isolated singularities $f_N := f + l^N$, where l is a general linear function and $N ∈ 𝔹$. We prove an attaching result of Iomdin-Lê type which compares the homotopy types of the Milnor fibres of $f_N$ and f. This is a refinement of the Iomdin-Lê theorem in the general setting of a singular underlying space.